`dy/dx = 10x^4-2x^3` Use integration to find a general solution to the differential equation above.

In order to use integration to solve this differential equation, multiply both sides of the equation by dx:

`dy = (10x^4 -2x^3)dx` .

Now we can integrate both sides, using the formula for the antiderivative of the power function: `int x^n = x^(n+1)/(n+1)`

`y = 10x^5/5 - 2x^4/4 + C`

Here, C is a constant. Since we are looking for a general solution of the equation which contains the first derivative, the solution has to include one arbitrary constant.

Simplifying the right side, we get

`y(x) = 2x^5 - x^4/2 + C` . This is the answer.